November 20, 2022 Dataset Open Access

Bartlett, Deaglan J.; Desmond, Harry; Ferreira, Pedro G.

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    <subfield code="a">DJB is supported by the Simons Collaboration on ``Learning the Universe'' and was supported by STFC and Oriel College, Oxford. HD is supported by a Royal Society University Research Fellowship (grant no. 211046). PGF acknowledges support from European Research Council Grant No: 693024 and the Beecroft Trust.</subfield>
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    <subfield code="a">Ferreira, Pedro G.</subfield>
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    <subfield code="u">CNRS &amp; Sorbonne Université, Institut d'Astrophysique de Paris and Astrophysics, University of Oxford</subfield>
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    <subfield code="a">Bartlett, Deaglan J.</subfield>
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    <subfield code="a">Exhaustive Symbolic Regression Function Sets</subfield>
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    <subfield code="a">&lt;p&gt;ESR (Exhaustive Symbolic Regression) is a symbolic regression algorithm which efficiently and systematically finds all possible equations at fixed complexity (defined to be the number of nodes in its tree representation) given a set of basis functions.&amp;nbsp;This is achieved by identifying the unique equations, so that one minimises the number of equations which one would have to fit to data.&lt;/p&gt;

&lt;p&gt;Here we provide the functions generated, the unique equations, and the mappings between all equations and unique ones&amp;nbsp;using different sets of basis functions. These are:&lt;/p&gt;

&lt;ul&gt;
	&lt;li&gt;&amp;quot;core_maths&amp;quot;:&amp;nbsp;&lt;span class="math-tex"&gt;\(\{x, a, {\rm inv}, +, -, \times, \div, {\rm pow} \}\)&lt;/span&gt;&lt;/li&gt;
	&lt;li&gt;&amp;quot;ext_maths&amp;quot;:&amp;nbsp;&lt;span class="math-tex"&gt;\(\{x, a, {\rm inv}, \sqrt{\cdot}, {\rm square}, \exp, +, -, \times, \div, {\rm pow} \}\)&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;where &lt;span class="math-tex"&gt;\(x\)&lt;/span&gt;&amp;nbsp;is the input variable and &lt;span class="math-tex"&gt;\(a\)&lt;/span&gt;&amp;nbsp;denotes a constant.&lt;/p&gt;

&lt;p&gt;One can fit these functions to a data set of interest by using the &lt;a href="https://esr.readthedocs.io"&gt;ESR package&lt;/a&gt;.&lt;/p&gt;</subfield>
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